Question

How do i simplify this

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \cfrac{3^4}{3^6} \right)^2\implies \left( \cfrac{3^{4\cdot 2}}{3^{6\cdot 2}} \right)\implies \cfrac{3^8}{3^{12}}\implies \cfrac{1}{3^{12}\cdot 3^{-8}}\implies \cfrac{1}{3^{12-8}}\implies \cfrac{1}{3^4}\implies \cfrac{1}{81}$